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FRM Part I · FRM Exam Part I · Country Risk: Determinants, Measures, and Implications

A 5-year sovereign CDS on Country W has a spread of 360 bps. Assume a recovery rate of 40% and a constant annual hazard rate, using the approximation spread = hazard rate x (1 - recovery). The annual risk-neutral default probability is approximately, and the implied 5-year cumulative risk-neutral default probability is closest to:

Dividing the 3.6% spread by the 60% loss given default gives a 6.0% annual default probability. Over five years, survival is 0.94 to the fifth power, about 73.4%, so cumulative default probability is about 26.6%. Simply multiplying by five overstates it at 30%.

  1. A6.0% per year; 26.6% cumulativeCorrect
  2. B6.0% per year; 30.0% cumulative
  3. C3.6% per year; 16.6% cumulative
  4. D9.0% per year; 37.4% cumulative

Explanation

Hazard = 0.036/(1-0.40) = 0.06 = 6.0% per year. Cumulative 5-year probability = 1 - exp(-0.06x5) = 1 - exp(-0.3) = 1 - 0.7408 = 25.9%; with discrete annual compounding, 1 - 0.94^5 = 1 - 0.7339 = 26.6%. The 30% option simply multiplies 6% by 5, ignoring compounding of survival. 3.6% ignores recovery.

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